Presentation I – Introduction to Quantity

Ask the child: “Do you remember what this is? Yes it is ten.” Slide the bar to the left of the mat.

Place 2 ten bars side by side in the middle: “What do we have here? Yes, two tens. Two tens are twenty. This is ten and this is twenty.” Slide the bars over near the ten bar leaving a slight space between them.

Lay 3 ten bars in front of you: “ten, twenty and thirty. Three tens make thirty.” Slight over to the right of twenty.

Review the names with a 3 period lesson.

Introduce the rest of the quantities in this manner decreasing repetition of the early quantities as the child retains them. Involve the child more and more: “What do you think we should get out next? Can you count that out?”

Play mix up and hiding games to reinforce and make the work fun.

Presentation II – Introduction to Symbols with Ten Boards

Invite the child to learn the symbols for tens. Spread the mat and boards in the same manner as the teen boards.

Be seated on one side with the child seated on the other.

Point to ten: “Do you remember what this is? Yes, it is ten.”

Point to 20: “Do you remember what this is? Yes, it is 20. Can you say 20?”

Point to 30: “Do you remember what this is? Yes, it is 30. Can you say 30?”

Continue introducing symbols and reviewing old ones. Check the child’s knowledge of the symbols. No need to give a lesson if the child already knows the symbol. Proceed to associate quantity when the child is ready.

Presentation III – Association of Quantity and Symbol

Invite child, spread out the mat and set out boards. Place bead bars at the upper left.

Ask the child to read the top numeral and to place a ten bar next to it. Continue placing quantities and reading quantities.

Try to have the child do most of the work. To reinforce, mix up the ten bars and have the child reorder.

Presentation IV – Counting to 99

Invite child to learn how to count to 99.

Spread mat, get materials and arrange as in previous presentations.

Put a ten bar to the left of the ten: “This is ten.”

Place the ten bar next to ten on the board.

Put one bead beside the ten bar: “This is eleven. Will you count with me?” Slide the numeral one over the zero: “This is how we write eleven.”

Place a second unit under the 1st: “This is twelve. Let’s count to twelve.”

Slide the numeral two over the zero: “This is how we write twelve.”

Place a third unit under the 2nd: “This is thirteen. Let’s count to thirteen.”

Slide the numeral three over the zero: “This is how we write thirteen.”

Continue adding units and changing symbol.

The child should take over at some point.

When you get to 19, ask the child what comes next: “Twenty comes next.”

Pick up the units and place them in their container. Place another ten bar to the right of the first ten bar, touching it: “This is twenty. This is how we write twenty.”

Place a unit next to the right of the tens: “This is twenty-one.”

Continue in this manner up to 99. This may take a few days. Allow the child to take breaks.

The Montessori Math Small Bead Frame is often neglected in Early Childhood classrooms. The frame comes at the end of the Place Value and Decimal System lessons, and, as noted by Dr. Montessori, marks the entrance into abstraction. Many classrooms do not get to the lesson for one reason or another. The lesson is meant for older children (5 1/2 and up) so that explains the dust a bit.

Montessori Small Bead Frame

Additionally, like my son's teacher, some teachers find the bead frame confusing to children. I personally really like the Small Bead Frame. The colors remind us of the place values, and I appreciate how children need to move their fingers as they are thinking, counting, and performing math operations. I particularly find the exchanging portion of the lesson effective with truly ingraining the concepts of place value into children's minds.

The goal of the lesson is to reinforce lessons a child has had on the four operations, bring more clarity to the ideas of place value, and to show the relationship between those values in the decimal system.

Presentation I: Introduction to the Small Bead Frame

Invite the child to learn how to use the bead frame. Gather the small bead frame and the presentation tray of the golden beads.

“The top row represents units. Will you take the unit from the presentation tray?” Point out the 1 on the top left of the frame.

Count the beads as you slide them to the right. Use your right index finger. Encourage the child to count the beads with you.

Point to the second row: “What do you think these stand for?”

Ask the child to retrieve a ten bar from the presentation tray.

Count the tens one by one. Say “ten, twenty, thirty…” or “one bar, two bars, three bars…” Proceed with the hundred row.

Ask the child to retrieve the hundred square from the presentation tray.

Count “one hundred, two hundred, three hundred…”

Continue with the thousand cube.

Name a quantity of units and ask the child to form it on the bead frame. Continue with tens, hundreds and thousands. Include numerals with zeros.

You can also use strips of paper to write a numeral and have the child use the bead frame to represent the numeral.

The overview of Montessori golden beads continues the child down the path of learning place value and the decimal system. The goal for the child is to garner a sense of quantities represented in the decimal system, and to see the exchange of quantities as units become ten, tens become hundred, and so on. This lesson is generally for 5 years and older.

Montessori Golden Beads Presentation I

Transition from Bead to Wooden Material

Introducing the wooden material very simply transitions the child from bead to wooden material.

Montessori Golden Beads Presentation II

Explain to the child that this work requires two mats. Have the child help spread the mats. Get the container of the units and begin to count them.

Place the units in a well-spaced vertical line at the right side of the mat.

Put one unit at the top: “one unit”.

Then two units next in line: “one, two units”.

Place three units next in line: “one, two, three units”.

The child takes over at this point.

At nine units explain, “You have nine units. What comes next? Yes, ten. So we need a ten bar instead of ten units. We also move to a new place.”

Get out the ten bars and start a vertical row to the left of the units. Proceed in a similar manner to presenting the units.

After the 9th set of ten bars, “Now, you’ve lined up nine ten bars, what do you need next? Right, hundreds. Where will you put the hundreds. That is right. We have to put them in a new place.”

Have the child bring the hundred squares. Lay out the hundred squares in a vertical row. Introduce in a similar manner as the units and the tens.

After nine hundreds, ask the child what comes next and where it goes. Ask her to bring thousand cubes over to the mat.

Introduce the thousand cubes in a similar manner to the units, the tens and the hundreds. The cubes are stacked on top of one another. Once all the cubes are stacked, invite the child to stand at the bottom

Variations

Question the child about the place values as he admires the finish work

Ask the child to point out various quantities on the mat

Have the child “teach” another child from the classroom

Child can place quantities “randomly” or two at a time rather than all the units at once

The Montessori Math Stamp Game lesson comes at the end of Place Value and Decimal System work. The goal is to reinforce the four operations introduced with the Golden Beads but in a more abstract way. I really like Montessori Math's Stamp Game. Children do, too. The work is familiar to them, but different enough to keep it interesting and intriguing. Montessori Printshop has great, go to download and print, Stamp Game worksheets to accompany the learning for FREE on their website. They also offer FREE Stamp Game instructions and materials.

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Montessori Math Stamp Game Lesson

Invite the child to a lesson with the Stamp Game.

Gather the Presentation Tray and a Stamp Game. Open the lid of stamps and place it under the box:

“This is the Stamp Game. It works like the Golden Beads, but instead of unit beads we have these unit stamps. Instead of ten bars we have these ten stamps. Instead of hundred squares we have hundred stamps. Instead of thousand cubes we have thousand stamps. Can you give me 5 ten stamps, 4 unit stamps,…?”

Practice until the child is quick at identifying the stamps.

Addition – Static

“Now let’s do some addition. I will write down an equation for you and you can use the stamps to solve it.”

Show the child how to line up stamps for the first, then the second addend in vertical columns.

Slide each column together to the bottom of the work area, count and record.

Ask the child to summarize his work for you at the end.

Give any directions needed to guide the child with the equations. Watch the child and then withdraw from the work.

Addition – Dynamic

The child should be able to move onto this work quickly. Watch her to see if she needs guidance with exchanging ten of one quantity for the next highest quantity. The new stamp goes to the top of its column, and is slid down and added to the two addends when the time comes.

Multiplication – Simple

Write an equation for the child, have her put out the quantity required in vertical columns. Remind her to start with the units.

Slide quantities together and to the bottom of work area.

Count and record answer.

Multiplication – Dynamic

{Process same as GB operation.}

Exchanging is done exactly as was described for addition.

Subtraction – Simple

{Process same as GB operation.}

Invite the child to get the appropriate number of stamps for the minuend.

Have her take away the number of units, tens, hundreds and thousands specified by the subtrahend by counting up from the bottom of the column of stamps.

These stamps should be removed from the work area by placing to the side.

Move the remaining stamps to bottom of mat.

Count and record each category.

Subtraction – Dynamic

{Process same as GB operation.}
Follow the same procedure as described for golden beads. When exchanging is required, go to next column to borrow a stamp, exchange it, place exchanged stamps in the appropriate column and proceed with subtraction.

Division – Static

Write an equation for the child and introduce the skittles: “You can use a skittle for each person you are dividing among. Why do you think the skittles are green? The reason is because they are units. Each skittle represents one person.”

Have child get out dividend. Arrange the skittles in a vertical row.

Beginning with the thousand stamps, distribute them one by one among the skittles. Then divide hundreds, tens and units.

This post includes a Montessori Math lesson for the Addition Snake Game. This Addition Snake lesson is found within Math Facts or Memorization of Montessori Math. Typically children towards the end of their Montessori Early Childhood career will be given this lesson. Amazon offers a few reasonably priced Addition Snake Game products.

Montessori Math Addition Snake Game

Once you have brought the materials to a work mat, the first part of the Montessori Math Addition Snake Game presentation is to create two short bead stairs.

Presentation One: Search for Ten

You create one right side up {with the nine bar at the base}. Have the child create the other triangle inverted.

“Now let’s make a snake with these colored beads. I’ll take the top bar from this triangle to start the snake. You take the top bar from the other triangle and put it next to the bar I placed on the mat.”

“Now we’re going to change the colored snake into a golden snake.”

Using a counter, begin counting from the first bead bar. Place the counter at the end of the tenth bead.

Roll the first two bead bars slightly out of the line and into a position below the colored snake.

Place a golden bar next to these beads and point out: “these are the same quantity so we can change the colored beads for the golden beads.”

Touch each bead with the counter as you count.

Repeat the process until the entire colored snake is replaced by golden beads. Move the colored beads back into a triangle or in a discard pile.

Line up the ten bars in the snake and count by tens to find the length of the snake. Offer the child a turn.

Presentation Two: Black & White Bead Stair

Make a long colored snake with the bars in random order.

Tell the child to begin changing the colored snake into a golden one: “but remember the golden beads can replace only how many colored beads at a time?”

When the child reaches ten, have him place a notched counter after that bead.

Roll the counted beads out of the snake. Place a golden ten bar under the beads that were counted.

Count the colored beads after the counter and say: “we can use the black and white beads to save the space of these beads.” Place the appropriate black and white beads after the golden bar.

Roll the golden and black bars back into the snake.

Place the colored beads aside.

Begin counting to ten again, starting with the black and white bar. Roll the bars out when you get to ten, replace the first ten with a golden bar, count the remaining beads and replace with a black and/or white bar.

Roll back into the snake. Place the colored beads aside and the black and white beads back into the triangle.

Continue with the approach until all the colored beads are changed to golden.

Count the whole snake by tens. Add on any black and white bar left at the tail of the snake.

Show the child how to check his work. Line up the golden bars vertically across the mat. Sort the colored beads in descending quantity from nine to one. Match a nine bar to a golden bar and ask the child what to put with the nine bar to make ten. Place a one bar with the nine bar. Continue.

This post include a lesson on Montessori Math Number Rod Addition. Montessori Small Number Rods are a favorite of preschoolers because the material is familiar and they get to do something different with it. This lesson comes at the end of a child's Early Childhood Montessori life. The Montessori Math Lesson with the Number Rods is within the area of “Math Facts” or “Memorization”.

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Invite child to do something new with the number rods.

Montessori Math Number Rod Addition

Ask him to spread a mat and build the stair with the number rods.

Separate the ten rod from the others: “Do you remember what this is? Yes, it is ten. Let’s see if there are other ways to make ten.”

Take the nine rod and place it against the ten rod: “What do we need to make this rod ten?” Allow the child the time to discover the answer.

Place the one rod in position and note that 9 + 1 = 10.

Have the child write this answer in his equation booklet.

See if the child can find a way to make ten with the eight rod.

Continue in this manner until he has discovered all possible ways of making ten.

Next, ask the child explore to find all the ways of making 9. Get him started if necessary by placing the eight rod against the 9 rod and asking what he needs to make it nine.

Over time give the child challenge cards that request he make combinations of eight, seven, six, five and so on. Make sure he records his work in a “Ways of making…” booklet.